# Electromagnetic energy in multilayered spherical particles

## TL;DR

This paper derives exact analytical formulas for electromagnetic energy distribution in multilayered spherical particles, applicable to both dielectric and magnetic media, with practical MATLAB code provided.

## Contribution

It introduces a recursive transfer-matrix method for precise energy calculations in multilayered spheres, including special cases and magnetic media.

## Key findings

- Analytic expressions for energy density inside and outside multilayered spheres.
- Explicit formulas for lossless core and shell configurations.
- Demonstrations of electric field enhancement in silica-gold multilayered spheres.

## Abstract

We obtain exact analytic expressions for (i) the electromagnetic energy radial density within and outside a multilayered sphere and (ii) the total electromagnetic energy stored within its core and each of its shells. Explicit expressions for the special cases of lossless core and shell are also provided. The general solution is based on compact recursive transfer-matrix method and its validity includes also magnetic media. The theory is illustrated on the examples of electric field enhancement within various metallo-dielectric silica-gold multilayered spheres. User-friendly MATLAB code which includes the theoretical treatment, is available as a supplement to the paper.